The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
Bounded treewidth as a key to tractability of knowledge representation and reasoning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Parameterized Complexity
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An important goal of research in description logics (DLs) and related logic-based KR formalisms is to identify the worst-case complexity of reasoning. Such results, however, measure the complexity of a logic as a whole. For example, reasoning in the basic DL ALCI is ExpTime-complete, which means that ALCI constructors can be used in a way so that exponential time is strictly required for solving a reasoning problem. It is, however, well known that, given two ALCI knowledge bases of roughly the same size, reasoning with one knowledge base may be much more difficult than with the other, depending on the interaction of the axioms in the KBs. Thus, existing worst-case complexity results provide only a very coarse measure of reasoning complexity, and they do not tell us much about the "hardness" of each individual knowledge base.